We describe a branch and cut algorithm for both MAX-SAT and weighted MAX-SAT. This algorithm uses the GSAT procedure as a primal heuristic. At each nodewe solve a linear programming (LP) relaxation of the problem. Two styles of separating cuts are added: resolution cuts and odd cycle inequalities. We compare our algorithm to an extension of the Davis Putnam Loveland (EDPL) algorithm and a Semi-Definite Programming (SDP) approach. Our algorithm is more effective than EDPL on some problems, notably MAX-2-SAT. EDPL and SDP are more effective on some other classes of problems.

Abstract. In recent years we have seen an increasing interest in combining constraint satisfaction problem (CSP) formulations and linear programming (LP) based techniques for solving hard computational problems. While considerable progress has been made in the integration of these techniques for solving problems that exhibit a mixture of linear and combinatorial constraints, it has been surprisingly difficult to successfully integrate LP-based and CSP-based methods in a purely combinatorial setting. Our approach draws on recent results on approximation algorithms based on LP relaxations and randomized rounding techniques, with theoretical guarantees, as well on results that provide evidence that the runtime distributions of combinatorial search methods are often heavy-tailed. We propose a complete randomized backtrack search method for combinatorial problems that tightly couples CSP propagation techniques with randomized LP-based approximations. We present experimental results that show that our hybrid CSP/LP backtrack search method outperforms the pure CSP and pure LP strategies on instances of a hard combinatorial problem. 1.

Abstract. We study the quality of LP-based approximation methods for pure combinatorial problems. We found that the quality of the LPrelaxation is a direct function of the underlying constrainedness of the combinatorial problem. More specifically, we identify a novel phase transition phenomenon in the solution integrality of the relaxation. The solution quality of approximation schemes degrades substantially near phase transition boundaries. Our findings are consistent over a range of LPbased approximation schemes. We also provide results on the extent to which LP relaxations can provide a global perspective of the search space and therefore be used as a heuristic to guide a complete solver.

Discovering interacting proteins is essential for understanding protein functions in a systematic fashion. However, high throughput interaction data are inherently noisy and only cover a small portion of the interactom. The question- can we infer useful protein-protein interaction information from those high throughput data- arises.

A (0; 1) matrix A is said to be ideal if all the vertices of the polytope Q(A) = fx : Ax 1; 0 x 1g are integral. The issue of finding a satisfactory characterization of those matrices which are minimally non-ideal is a well known open problem. An outstanding result toward the solution of this problem, due to Alfred Lehman, is the description of crucial properties of minimally non-ideal matrices. In this paper we consider the extension of the notion of ideality to (0; \Sigma1) matrices. By means of a standard transformation, we associate with any (0; \Sigma1) matrix A a suitable (0; 1) matrix D(A). Then we introduce the concept of disjoint completion A + of a (0; \Sigma1) matrix A and we show that A is ideal if and only if D(A + ) is ideal. Moreover, we introduce a suitable concept of a minimally non-ideal (0; \Sigma1) matrix and we prove a Lehman-type characterization of minimally non-ideal (0; \Sigma1) matrices. 1 Introduction Let A be a (0; \Sigma1) matrix whose sets of ...

This paper introduces a hybrid genetic algorithm for the satisfiability problem (SAT). This algorithm, called GASAT, incorporates local search within the genetic framework. GASAT relays on a problem specific crossover operator to create new solutions, that are improved by a tabu search procedure. The performance of GASAT is assessed using a set of well-known benchmarks. Comparisons with state-of-the-art SAT algorithms show that GASAT gives competitive results.